The convex hull of a Banach-Saks set Articles uri icon

authors

  • LOPEZ-ABAD, J.
  • RUIZ, C.
  • TRADACETE PEREZ, PEDRO

publication date

  • February 2014

start page

  • 2251

end page

  • 2280

issue

  • 4

volume

  • 266

International Standard Serial Number (ISSN)

  • 0022-1236

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

abstract

  • A subset A of a Banach space is called Banach-Saks when every sequence in A has a Cesaro convergent subsequence. Our interest here focuses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a combinatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result. (C) 2013 Elsevier Inc. All rights reserved.

keywords

  • banach-saks property; convex hull; schreier spaces; ramsey property; property; summability; sequences; spaces